Exponentially fitted variants of Newton's method with quadratic and cubic convergence

In this paper, we present some new families of Newton-type iterative methods, in which f′(x)=0 is permitted at some points. The presented approach of deriving these iterative methods is different. They have well-known geometric interpretation and admit their geometric derivation from an exponential fitted osculating parabola. Cubically convergent methods require the use of the first and second derivatives of the function as Euler's, Halley's, Chebyshev's and other classical methods do. Furthermore, new classes of third-order multipoint iterative methods free from second derivative are derived by semi-discrete modifications of cubically convergent iterative methods. Further, the approach has been extended to solve a system of non-linear equations.     

LAWS OF FORM AND FINITE AUTOMATA

G. Spencer Brown's book Laws of Form informally presents three distinct logical systems. The third system is interpreted here through Alonzo Church's restricted recursive arithmetic. Restricted recursive arithmetic was introduced by Church in 1955 as the first formal system capturing finite automata. It is suggested that this interpretation is closer to Spencer Brown's original ideas than the interpretation with three-valued logic given by Francisco Varela.     

一种计算机辅助评估儿童急性淋巴细胞白血病预后新方法

介绍一种计算机辅助评估儿童急性淋巴细胞白血病预后的新方法,并对该方法的原理及主要步骤进行了详细阐述和分析.通过检验,所得结果与医务人员的结论一致,证明了该方法的可行性.     

基于覆盖算法的白血病微阵列判别方法

微阵列数据的一个重要应用就是给疾病样本分类。微阵列数据具有样本数量小、特征数量大的特点。该文提出了一种新的方法。以急性白血病的基因表达数据为对象,经过t统计法适当降维,利用覆盖算法白血病类型进行分类,并同已有算法进行了对比。实验结果证明本算法是有效的。     

企业部门防御结构体系的实现*

网络安全防范不仅要抵御外来攻击,更要防止内部泄密。利用VPN技术,为数据传输建立私有通道,实现数据端到端的加密传输。通过在一个企业VPN内建立部门VPN,把私有传输通道延伸到企业内各部门间,有效防止各部门重要数据从企业网络内部泄漏。     

FLAWS OF FORM

G. Spencer Brown's book Laws of Form has been enjoying a vogue among social and biological scientists. Proponents claim that the book introduces a new logic ideally suited to their fields of study, and that the new logic solves the problems of self-reference. These claims are false. We show that Brown's system is Boolean algebra in an obscure notation, and that his “solutions” to the problems of self-reference are based on a misunderstanding of Russell's paradox.     

六分量天平在救生伞空投试验中的应用研究

针对飞行员救生伞高速空投试验开伞力测试不真实的问题,通过分析拉力传感器和过载传感器测试方法影响高速试验开伞力测试结果的机理,提出了含有六分量天平的测试布局,并研制了专用的杆式六分量天平,经过空投试验实际应用表明,该方案可以显著减小外界因素对测试结果的影响,能够更真实的反应测试假人承受开伞力的状态.     

Numerical solution of laplace's equation on non-simply connected regions on R 2

We consider the interior Dirichlet problem for Laplace's equation on a non-simply connected two-dimensional regions with smooth boundaries.The solution is sought as the real part of a holomorphic function on the region, given as Cauchy-type integral.The approximate double layer density function is found by solving a system of Fredholm integral equations of second kind.Because of the non-uniqueness of the solution of the system we solve it using a technique based on the solution of the “Modified Dirichlet problem”.The Nystrom's method coupled with the trapezoidal rule is used as numerical integration scheme.The linear system derived from the integral equation is solved using the conjugate gradient applied to the normal equation.Theoretical and computational details of the method are presented.     

Optimal equi-scaled families of Jarratt's method

In this paper, we present many new fourth-order optimal families of Jarratt's method and Ostrowski's method for computing simple roots of nonlinear equations numerically. The proposed families of Jarratt's method having the same scaling factor of functions as that of Jarratt's method (i.e. quadratic scaling factor of functions in the numerator and denominator of the correction factor) are the main finding of this paper. It is observed that the body structures of our proposed families of Jarratt's method are simpler than those of the original families of Jarratt's method. The efficiency of these methods is tested on a number of relevant numerical problems. Furthermore, numerical examples suggest that each member of the proposed families can be competitive to other similar robust methods available in the literature.